I actually have been doing some more serious observations of water temps in a yuzamashi (taller version) based upon discussion in two other current topics ... and some cursory observations I had noticed for quite some time while using a digital thermometer (DT) that registersw readings very quickly (some DTs are much slower).

Today (temps in F):

First I placed the digital thermometer probe (DTP) all the way in and it is resting upon the bottom, 150-155*

Raising the DTP even slightly off the bottom instantly raises the temp 10ish* to 160-165*

Slowly raising the DTP upward the reading gradually rises as well.

As I near the surface, maybe an inch deep, the temp is hottest, 175-180*

Then as the DTP gets closer and closer to the surface, the temp decreases slightly.

< 1/4" deep the temp is still around 165-170* (I will try to get as shallow as possible and see if I still get a reading)

Almost all the differences in temp are rather alleviated by swirling the water a little bit with the DTP, but still the bottom surface remains much cooler. Even <1/4" deep gives a very similar reading as plunged deeply into the Yuzamashi. Similarly, raising the Yuzamashi and swirling the entire thing has the same effect. Allowing the Yuzamashi to sit again, the differentiation again occurs, but not as dramatically.

Temperatures within the Yuzamashi can vary greatly and swirling generally helps to obtain an accurate overall reading

The DTP gives pretty accurate readings even by only touching the bottom or even barely being in the water, it is the very tip that seems most critical ... not what conventional wisdom or directions indicate.

Thanks, Chip. That is useful info & interesting. Of course, we know that heat rises to the top, but I would not have guessed at the amount of difference that you measured.However, I often stir teapots, even when preparing tea w/ short infusions. I want all of the tea to be working w/ the water (& at the correct steeping temperature). I remember snorkeling in the ocean 25' down. Coming up for air, I'd sometimes notice a few differences in temperature, & it was not always cooler at the lower depths.

Later today I tested similarly with a shallow Shiboridashi from Petr. This showed much much less variability I am guessing partly due to being so shallow, but also the bottom is much thinner and may heat up quicker than the thick bottomed one I used in the OP test.

Preheating the yuzamashi and swirling the water around should make sure temperatures are more evenly distributed. You need the walls of the yuzamashi to be nearly as hot as the water that you pour in it in order for temperature variations to be minimized. Of course it will take longer to cool down the water that you'll be using for your tea.